Stochastic Simulation of Environmental Random Processes
Date Issued
2008
Date
2008
Author(s)
Liou, Jun-Jih
Abstract
Uncertainty analysis using stochastic simulation is an essential task in modeling environmental random processes. It is particularly important when the data under investigation is non-Gaussian, and available only at limited spatial or temporal points – the situation of having insufficient information in stochastic characteristics of environmental variables. This dissertation presents three innovative stochastic simulation approaches to tackle uncertainties involved in three important topics in environmental modeling – (1) L-moment based goodness-of-fit (GOF) test, (2) gamma-random-field simulation, and (3) Markov chain simulation of random fields with anisotropic exponential variogram model. For the L-moment based GOF test, 95% acceptance region of the moment ratio diagram was established for both normal and Gumbel distributions. These acceptance regions are sample-size dependent, and, through stochastic simulation, empirical formulae for construction of 95% acceptance region with respect to arbitrary sample size between 20 and 1000 were established. For Gamma random field simulation, a theoretical relationship between the covariance functions of a gamma random field and its corresponding standard normal random field was derived. Then, through a gamma-to-Gaussian covariance matrix conversion, a sequential Gaussian random filed simulation was conducted using the required Gaussian covariance matrix. Finally, realizations of the gamma random field were generated by a Gaussian-gamma transformation. For random fields with exponential variogram model, a Markov chain simulation approach proposed in this study is shown to be more efficient and can be applied for anisotropic random field simulation.
Subjects
uncertainty analysis
environmental random processes
goodness-of-fit test
linear-moment method
gamma random field
Markov chain random field
Type
thesis
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